The photo is not sent with the message. The Mail.app on a Mac includes the same - the photo for contact info in the Address Book. If a message is sent to a recipient using the Mail.app on a Mac or using an iPad, the recipient's chosen photo for your contact info in their address book is shown with the received message, and the same in reverse on your iPhone.
Are you saying you have no contact info in your iPad's address book? If not, is your contact info available in your iPad's address book? If so, do you have a photo selected for your contact info?
Are you saying you have no contact info in your iPad's address book? If not, is your contact info available in your iPad's address book? If so, do you have a photo selected for your contact info?